This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A182260 #20 Jan 05 2025 12:31:09
%S A182260 0,3,11,28,56,99,159,240,344,475,635,828,1056,1323,1631,1984,2384,
%T A182260 2835,3339,3900,4520,5203,5951,6768,7656,8619,9659,10780,11984,13275,
%U A182260 14655,16128,17696,19363,21131,23004,24984,27075,29279,31600,34040
%N A182260 Number of ordered triples (w,x,y) with all terms in {1,...,n} and 2w<x+y.
%C A182260 Also the number of ordered triples (w,x,y) with all terms in {1,...,n} and 2w>x+y.
%C A182260 A182260(n)+A055232(n)=3^(n-1).
%C A182260 A182260 is row 1 of A211802 and also row 1 of A182259; see A211790 for a discussion and guide to related sequences.
%H A182260 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2,-2,3,-1).
%F A182260 a(n) = 3*a(n-1)-2*a(n-2)-2*a(n-3)+3*a(n-4)-a(n-5).
%F A182260 From _Colin Barker_, May 06 2012: (Start)
%F A182260 a(n) = (-1+(-1)^n-2*n^2+4*n^3)/8.
%F A182260 G.f.: x^2*(3 + 2*x + x^2)/((1 - x)^4*(1 + x)). (End)
%e A182260 For n=2, the 3 triples (w,x,y) for which 2w<x+y are (1,1,2), (1,2,1), (1,2,2). The 3 triples for which 2w>x+y are (2,1,1), (2,1,2), (2,2,1).
%t A182260 (See the program at A211802.)
%t A182260 LinearRecurrence[{3,-2,-2,3,-1},{0,3,11,28,56},50] (* _Harvey P. Dale_, Aug 10 2019 *)
%Y A182260 Cf. A211790, A211802.
%K A182260 nonn,easy
%O A182260 1,2
%A A182260 _Clark Kimberling_, Apr 22 2012